• Accepted Paper

Activation and avalanche length scales in the finite-temperature creep of an elastic interface

Giovanni Russo, Ezequiel E. Ferrero, Alejandro B. Kolton, Alberto Rosso, and Damien Vandembroucq

Phys. Rev. Lett. - Accepted 28 October, 2026

DOI: https://doi.org/10.1103/51r8-1rnf

Abstract

We investigate the creep dynamics of a driven elastic line at finite temperature, well below the depinning threshold. We show that creep is governed by two distinct length scales. The first, ℓopt, corresponds to the optimal activated rearrangements that control the dynamics’ bottleneck and remains essentially temperature-independent. The second, ℓav, characterizes the spatial extent of thermally activated avalanches and grows as temperature decreases. By combining structural and dynamical observables, we show that ℓav governs both the crossover in the structure factor and the growth of the four-point dynamical susceptibility, while the relaxation time remains controlled by activation over large barriers associated with ℓopt. We find that the avalanche scale follows ℓav(T ) ∼ T −νdep, thereby selecting a unique scenario among competing theoretical predictions. These results establish a unified picture of finite-temperature creep in which activation controls temporal scales while depinning criticality governs spatial correlations.

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